Solve for $x$ : $x^2 + 10x + 24 = 0$
Explanation: The coefficient on the $x$ term is $10$ and the constant term is $24$ , so we need to find two numbers that add up to $10$ and multiply to $24$ The two numbers $4$ and $6$ satisfy both conditions: $ {4} + {6} = {10} $ $ {4} \times {6} = {24} $ $(x + {4}) (x + {6}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 4) (x + 6) = 0$ $x + 4 = 0$ or $x + 6 = 0$ Thus, $x = -4$ and $x = -6$ are the solutions.